Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems

The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and the solution of split feasibility problems (SFP) and systems of equilibrium problems (SEP) in Hilbert spaces. We prove that the sequences genera...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.108-115-511
Main Authors: Sombut, Kamonrat, Plubtieng, Somyot
Format: Article
Language:English
Subjects:
Algorithms
Convergence
Convergence (Mathematics)
Feasibility
Fixed point theory
Fixed points (mathematics)
Fuzzy sets
Hilbert space
Iterative algorithms
Mapping
Mathematical research
Optimization
Sequences
Set theory
Studies
Theorems
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Summary:The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and the solution of split feasibility problems (SFP) and systems of equilibrium problems (SEP) in Hilbert spaces. We prove that the sequences generated by the proposed algorithm converge weakly to a common element of the fixed points set of quasi-nonexpansive mappings and the solution of split feasibility problems and systems of equilibrium problems under mild conditions. Our main result improves and extends the recent ones announced by Ceng et al. (2012) and many others.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/430409